Abstract
We propose a numerical method for the multiple interface problems in this paper. In our method, we first construct a new space and prove it to be a reproducing kernel space; furthermore, the reproducing kernel function of the space is given simultaneously. Then, a set of the basis of the broken reproducing kernel space is constructed by utilizing the nature of the reproducing kernel function. Therefore, we can use the set of the basis to represent the approximate solution. To ensure the unknown coefficients to obtain the approximate solution of the equations and to prove the unknown coefficients are uniquely determined, we consider a system of algebraic linear equations. Furthermore, we discuss the error analysis of our method. Finally, the results of several numerical examples and the comparisons with some known methods prove that our method has better accuracy.
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Acknowledgements
This study was supported by National Natural Science Funds of China by Grant number 12101164; Harbin Normal University Postgraduate Innovative Research Project by Grant number HSDSSCX2022-40.
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Yu, Y., Yang, X., Cui, Y. et al. A broken reproducing kernel method for the multiple interface problems. Comp. Appl. Math. 41, 260 (2022). https://doi.org/10.1007/s40314-022-01963-7
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DOI: https://doi.org/10.1007/s40314-022-01963-7
Keywords
- Multiple interface problems
- Reproducing kernel method
- Broken reproducing kernel function
- A system of algebraic linear equations